What can I do to get my father released from the hospital if the hospital won't release him?

Hospitals today are very quick to release patients, so if they are not releasing your father, it must be for a very good reason, as in he is not ready for rehab yet. They normally will release him to skilled nursing when ready.

Also take into consideration, should you bring dad home early/dad leaves on his own from the hospital against medical advice (AMA), and he should suffer some sort of recent surgery-related emergency requiring another admittance, his insurance might not cover the cost of the second time admitted, if it's determined that, should he have remained as recommended the first time, those complications might not have happened.

I can understand why he's so eager to get out of the hospital; the question is, why are you so eager for him to get out before the hospital believes it is safe for him to do so?

I can only imagine that if the hospital won't release him it's because he is still unstable and not ready to be released yet. No one likes to stay in a hospital, but it's usually in the patients best interest to do so and until the doctors say otherwise. And insurance companies certainly won't allow the hospital to keep anyone longer than needed, so let the hospital/doctors do their job and when he is ready to be released, you can request that he be sent to rehab, or if no one can care for him at home, you can get the hospital social worker involved to have him placed in the appropriate facility.

What are his post-op care requirements?

I guarantee you the hospital is not just keeping him, there is a medical necessity or he would be discharged to a rehabilitation facility aka skilled nursing.

Have you spoken to his care team, surgeon? I would do that asap, get an idea of how long he will be required to stay, why he is still there and then explain to him what is going on.

Is he being treated for his anxiety? The hospital could address that if he isn't getting any meds to help.

Did they mention rehab?